(3x-6)(2x^2-7x+1)

2 min read Jun 16, 2024
(3x-6)(2x^2-7x+1)

Expanding the Expression (3x-6)(2x^2-7x+1)

This article will guide you through the process of expanding the expression (3x-6)(2x^2-7x+1). We will utilize the distributive property, often referred to as the FOIL method, to achieve this.

Understanding the FOIL Method

FOIL stands for First, Outer, Inner, Last. It's a mnemonic device used to remember the steps involved in multiplying two binomials. Here's how it works:

  1. First: Multiply the first terms of each binomial.
  2. Outer: Multiply the outer terms of the binomials.
  3. Inner: Multiply the inner terms of the binomials.
  4. Last: Multiply the last terms of each binomial.

Expanding the Expression

Let's apply the FOIL method to our expression (3x-6)(2x^2-7x+1):

  1. First: (3x) * (2x^2) = 6x^3
  2. Outer: (3x) * (-7x) = -21x^2
  3. Inner: (-6) * (2x^2) = -12x^2
  4. Last: (-6) * (-7x) = 42x
  5. Last: (-6) * (1) = -6

Now we combine all the terms:

6x^3 - 21x^2 - 12x^2 + 42x - 6

Finally, we combine the like terms:

6x^3 - 33x^2 + 42x - 6

Conclusion

By applying the FOIL method, we successfully expanded the expression (3x-6)(2x^2-7x+1) into a polynomial of degree 3. The final expanded form is 6x^3 - 33x^2 + 42x - 6.

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